From (7) and (9) it is clear that the only essential information contained in Ei is the set of values i\u and the index rt. Note further that in (8), the successive Ei are used with increasing I and it follows from (9) that it is necessary to know ri before using the r¡n. On the other hand, in (6), the E¡ are used in decreasing sequence of / but from (7) it is not necessary to know rt until aft...

In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...

We discuss the early history of B-splines with an arbitrary knot sequence, and of their recurrence relations. These seem to have first appeared in papers of Popoviciu and Chakalov from the 1930’s. key words B-spline, recurrence, divided difference